Can I cut out the texture part of an object?
If you are using armature for both objects you can just hide one of them in the Outliner. If you joined objects together and didn't connect any of their vertices then you can easily assign different materials to them from edit mode. Go to edit mode, mouse over one of the objects, press L (it should select only connected vertices, 1 object in your case), assign other material to faces from material tab (Assign button under list of object materials).